Low Energy Dynamics of the Spinon-Gauge System

The normal phase of the high-$T_c$ cuprates is apparently not described by Fermi liquid theory. It has been proposed that a dynamically generated gauge field must appear in the effective field theory. Even a simple spinon-gauge system is complicated, becoming strongly coupled at low energy. We show that in a large-$n$ approximation the theory can be solved and has a nontrivial fixed point. Also, we find that there is no antiferromagnetic instability at weak coupling.